Probing the single-particle behavior above Sn132 via electromagnetic moments of Sb133,134 and N=82 isotones

Abstract

Magnetic and quadrupole moments of the $7/{2}^{+}$ ground state in $^{133}\mathrm{Sb}$ and the $({7}^{\ensuremath{-}})$ isomer in $^{134}\mathrm{Sb}$ have been measured by collinear laser spectroscopy to investigate the single-particle behavior above the doubly magic nucleus $^{132}\mathrm{Sn}$. The comparison of experimental data of the $7/{2}^{+}$ states in $^{133}\mathrm{Sb}$ and neighboring $N=82$ isotones to shell-model calculations reveals the sensitivity of magnetic moments to the splitting of the spin-orbit partners $\ensuremath{\pi}0{g}_{9/2}$ and $\ensuremath{\pi}0{g}_{7/2}$ across the proton shell closure at $Z=50$. In contrast, quadrupole moments of the $N=82$ isotones are insensitive to cross-shell excitations, but require the full proton model space from $Z=50\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}82$ for their accurate description. In fact, the linear trend of the quadrupole moment follows approximately the expectation of the seniority scheme when filling the $\ensuremath{\pi}0{g}_{7/2}$ orbital. As far as the isomer in $^{134}\mathrm{Sb}$ is concerned, its electromagnetic moments can be perfectly described by the additivity rule employing the moments of $^{133}\mathrm{Sb}$ and $^{133}\mathrm{Sn}$, respectively. These findings agree with shell-model calculations and thus confirm the weak coupling between the valence proton and neutron in $^{134}\mathrm{Sb}$.